The Magic Trick of Physical Constants

🧵 TL;DR

The "fundamental constants" aren't what physics thinks they are.
They're not unexplained magic — they're the scaffolding of a coordinate transformation.
And when you rotate completely into Planck space, the universe speaks with one axis: time.

We're calling out the three-act structure of a foundational physics sleight of hand:

🎩 The Magic Trick of Physical Constants

1. The Pledge

“These constants — $c$, $G$, $h$, $k_B$ — are fundamental. They encode the deepest truths about physical reality. They are mysterious and irreducible."

This is the story we all get trained on. It sets the stage by making the constants look like pillars of natural law, mysterious but immutable, as if handed down by the universe itself.

2. The Turn

"We'll simplify physics by setting the constants equal to 1 in natural units."

This is where the trick is pulled: the magician distracts the audience. The constants that were once "deep truths" are conveniently removed from all equations via unit redefinition. Boom — now everything is dimensionless!

But what just happened?

What just happened is a full Jacobian rotation — a deliberate, structured collapse of SI measurement charts into a Planck coordinate basis, where all unit axes are rescaled and aligned with time or frequency.

But... nobody told the audience that — they’re too busy watching the card disappear.

3. The Prestige

“And lo: in Planck units, everything important becomes 1. At this scale, mass, energy, temperature, frequency, momentum... are all scaled to time.”

$$T = f = m = E = p = \frac{1}{l}$$

That's the real reveal:
Not that constants go away, but that the quantities they connect collapse into the same time axis, with different interpretations.

This is not trivial; it’s revealing something profound:

• Mass becomes the frequency scale (via $E = mc^2 = hf$)

• Energy becomes inverse time (via $E = \hbar \omega$)

• Temperature becomes energy (via $E = k_B T$)

• Momentum becomes inverse length (via $p = \hbar / \lambda$)

• And all of them collapse into the same dimensionless value at the Planck scale.

🧠 What You’re Actually Showing

You're demonstrating that at the Planck scale, the axes we perceive as separate in SI — mass, energy, temperature, frequency, momentum — are actually projections of a single fundamental measurement: length, or more accurately, inverse length.

And the so-called constants? They are just the Jacobian scaffolding needed to rotate from the human (SI) chart to that native system.

💣 Why This Reframes "Fundamentality"

You're showing:

• Constants are not irreducible truths. They are coordinate artifacts caused by projecting a unified structure onto multiple unit axes.

• The real structure is dimensionless — built entirely out of ratios.

• The appearance of mysterious, unrelatable axes (temperature vs. energy vs. mass) is a fiction of the SI coordinate basis.

In Planck units, the universe speaks one language — just rotated into many local dialects by our arbitrary choice of measurement system.

✊ Conclusion: Physics Without the Hand-Wave

• The “setting constants to 1” move is not wrong — it’s the end of the transformation, not the beginning.

• What is wrong is pretending it’s trivial — or worse, using it to obscure the fact that the constants themselves are the glue of unit-space rotation.

• This approach names the Jacobian, tracks it, exposes the hidden group structure in unit conversions — and completes the transformation honestly.

Every other axis is a rescaled dialect of that one fundamental idea.

We're not asking anyone to believe in a new theory.
We're just finishing the math they started — and never returned to.

Appendix A - Jacobian Rotation in Unit Space.

This is the proof cat modular/unit_scaling/planck_h_scaling.py 

https://github.com/BuckRogers1965/Physics-Unit-Coordinate-System/blob/main/examples/physics_unit_coordinate_scaling.py

import math

# Dynamically loads reusable modules from specified file paths to keep the program modular and extensible. from load_mods import load_module

# Define standard CODATA 2018 values for necessary constants in SI G   = 6.67430e-11 e   = 1.602176634e-19 c   = 299792458.0 k_B = 1.380649e-23 h   = 6.62607015e-34  k   = 1.3806490000e-23

Hz_kg = h / c2 K_Hz  = k / h G_n   = G * Hz_kg / c3 t_P   = G_n(1/2) e_scaling = (  1e7 * Hz_kg * c  )(1/2) #e_scaling = (  1e7 * Hz_kg * c )(1/2) * 3.4079462030e-02 (1/4) #e_scaling = (  1e7 * Hz_kg * c / 0.26397533357678554*(2))**(1/2) 

def calculate_scaling_factors(constants):

    rescale_factors = [         {"symbol": "s",  "factor": t_P,             "swap_with": "t_Ph"},         {"symbol": "m",  "factor": t_P * c,         "swap_with": "l_Ph"},         {"symbol": "kg", "factor": Hz_kg/t_P,       "swap_with": "m_Ph"},         {"symbol": "K",  "factor": 1/(t_P *  K_Hz), "swap_with": "T_Ph"},         #{"symbol": "C",  "factor": e_scaling,       "swap_with": "C_Ph"},         {"symbol": "A",  "factor": e_scaling / t_P, "swap_with": "A_Ph"},         {"symbol": "mol","factor": Hz_kg/t_P,       "swap_with": "mol_Ph"},         {"symbol": "pi", "factor": 1.0,             "swap_with": "pi"},         {"symbol": "amu","factor": 1.0,             "swap_with": "amu"},     ]

    composite_unit_module = load_module("./modular/composite_units.py", "composite_units")

    return composite_unit_module.rescale_composite_units(rescale_factors, "_Ph")

The output: python physics_unit_coordinate_scaling.py 

   Symbol   Constant Name                    Original Value   Rescaled Value   Units Applied                 Ratio    -----------------------------------------------------------------------------------------------------------------------------

   --- Core Scaling Constants ---    c        speed_of_light_c                 2.9979245800e+08 1.0000000000e+00 l_Ph t_Ph⁻¹                   2.99792458e+08    h        planck_constant_h                6.6260701500e-34 1.0000000000e+00 J_Ph t_Ph                     6.62607015e-34    Hz_kg    Hz_kg                            7.3724973238e-51 1.0000000000e+00 m_Ph Hz_Ph⁻¹                  7.37249732e-51    k        boltzmann_constant_k             1.3806490000e-23 1.0000000000e+00 m_Ph l_Ph² t_Ph⁻² T_Ph⁻¹      1.38064900e-23    K_Hz     K_Hz                             2.0836619123e+10 1.0000000000e+00 Hz_Ph T_Ph⁻¹                  2.08366191e+10    G        gravitational_constant_G         6.6743000000e-11 1.0000000000e+00 l_Ph³ m_Ph⁻¹ t_Ph⁻²           6.67430000e-11    k_e      coulombs_constant_k_e            8.9875517870e+09 9.9999999996e-01 m_Ph l_Ph³ t_Ph⁻² C_Ph⁻²      8.98755179e+09